Shaping Light in Nonlinear Optical Fibers

This book is a contemporary overview of selected topics in fiber optics. It focuses on the latest research results on light wave manipulation using nonlinear optical fibers, with the aim of capturing some of the most innovative developments on this topic. The book’s scope covers both fundamentals and applications from both theoretical and experimental perspectives, with topics including linear and nonlinear effects, pulse propagation phenomena and pulse shaping, solitons and rogue waves, novel optical fibers, supercontinuum generation, polarization management, optical signal processing, fiber lasers, optical wave turbulence, light propagation in disordered fiber media, and slow and fast light. With contributions from leading-edge scientists in the field of nonlinear photonics and fiber optics, they offer an overview of the latest advances in their own research area.  The listing of recent research papers at the end of each chapter is useful for researchers using the book as a reference. As the book addresses fundamental and practical photonics problems, it will also be of interest to, and benefit, broader academic communities, including areas such as nonlinear science, applied mathematics and physics, and optical engineering. It offers the reader a wide and critical overview of the state-of-the-art within this practical – as well as fundamentally important and interesting – area of modern science, providing a useful reference which will encourage further research and advances in the field.

Table of Contents:
List of Contributors xiii Preface xvii 1 Modulation Instability, Four-Wave Mixing and their Applications 1 Tobias Hansson, Alessandro Tonello, Stefano Trillo, and Stefan Wabnitz 1.1 Introduction 1 1.2 Modulation Instability 2 1.2.1 Linear and Nonlinear Theory of MI 2 1.2.2 Polarization MI (PMI) in Birefringent Fibers 7 1.2.3 Collective MI of Four-Wave-Mixing 9 1.2.4 Induced MI Dynamics, Rogue Waves, and Optimal Parametric Amplification 11 1.2.5 High-Order Induced mi 13 1.2.6 MI Recurrence Break-Up and Noise 14 1.3 Four-Wave Mixing Dynamics 17 1.3.1 FWM Processes with Two Pumps 17 1.3.2 Bragg Scattering FWM 18 1.3.3 Applications of BS-FWM to Quantum Frequency Conversion 20 1.4 Fiber Cavity MI and FWM 20 1.4.1 Dynamics of MI in a Passive Fiber Cavity 20 1.4.2 Parametric Resonances and Period Doubling Phenomena 23 1.4.3 FWM in a Fiber Cavity for Optical Buffer Applications 25 References 27 2 Phase-Sensitive Amplification and Regeneration 35 Francesca Parmigiani 2.1 Introduction to Phase-Sensitive Amplifiers 35 2.2 Operation Principles and Realization of Phase-Sensitive Parametric Devices 36 2.3 One-Mode Parametric Processes 40 2.4 Two-Mode Parametric Processes 54 2.5 Four-Mode Parametric Processes 56 2.6 Conclusion 58 Acknowledgments 59 References 60 3 Novel Nonlinear Optical Phenomena in Gas-Filled Hollow-Core Photonic Crystal Fibers 65 Mohammed F. Saleh and Fabio Biancalana 3.1 Introduction 65 3.2 Nonlinear Pulse Propagation in Guided Kerr Media 66 3.3 Ionization Effects in Gas-Filled HC-PCFs 67 3.3.1 Short Pulse Evolution 68 3.3.2 Long-Pulse Evolution 72 3.4 Raman Effects in Gas-Filled HC-PCFs 76 3.4.1 Density Matrix Theory 76 3.4.2 Strong Probe Evolution 82 3.5 Interplay Between Ionization and Raman Effects in Gas-Filled HC-PCFs 85 3.6 Conclusion 89 Acknowledgments 89 References 89 4 Modulation Instability in Periodically Modulated Fibers 95 Arnaud Mussot, Matteo Conforti, and Alexandre Kudlinski 4.1 Introduction 95 4.2 Basic Theory of Modulation Instability in Periodically Modulated Waveguides 96 4.2.1 Piecewise Constant Dispersion 100 4.3 Fabrication of Periodically Modulated Photonic Crystal Fibers 101 4.3.1 Fabrication Principles 101 4.3.2 Typical Example 101 4.4 Experimental Results 104 4.4.1 Experimental Setup 104 4.4.2 First Observation of Multiple Simultaneous MI Side Bands in Periodically Modulated Fibers 104 4.4.3 Impact of the Curvature of the Dispersion 105 4.4.4 Other Modulation Formats 107 4.5 Conclusion 111 Acknowledgments 111 References 111 5 Pulse Generation and Shaping Using Fiber Nonlinearities 115 Christophe Finot and Sonia Boscolo 5.1 Introduction 115 5.2 Picosecond Pulse Propagation in Optical Fibers 116 5.3 Pulse Compression and Ultrahigh-Repetition-Rate Pulse Train Generation 117 5.3.1 Pulse Compression 117 5.3.2 High-Repetition-Rate Sources 121 5.4 Generation of Specialized Temporal Waveforms 124 5.4.1 Pulse Evolution in the Normal Regime of Dispersion 124 5.4.2 Generation of Parabolic Pulses 125 5.4.3 Generation of Triangular and Rectangular Pulses 127 5.5 Spectral Shaping 128 5.5.1 Spectral Compression 129 5.5.2 Generation of Frequency-Tunable Pulses 132 5.5.3 Supercontinuum Generation 133 5.6 Conclusion 137 Acknowledgments 138 References 138 6 Nonlinear-Dispersive Similaritons of Passive Fibers: Applications in Ultrafast Optics 147 Levon Mouradian and Alain Barthélémy 6.1 Introduction 147 6.2 Spectron and Dispersive Fourier Transformation 150 6.3 Nonlinear-Dispersive Similariton 151 6.3.1 Spectronic Nature of NL-D Similariton: Analytical Consideration 152 6.3.2 Physical Pattern of Generation of NL-D Similariton, Its Character and Peculiarities on the Basis of Numerical Studies 153 6.3.3 Experimental Study of NL-D Similariton by Spectral Interferometry (and also Chirp Measurements by Spectrometer and Autocorrelator) 155 6.3.4 Bandwidth and Duration of NL-D Similariton 158 6.3.5 Wideband NL-D Similariton 159 6.4 Time Lens and NL-D Similariton 160 6.4.1 Concept of Time Lens: Pulse Compression—Temporal Focusing, and Spectral Compression—“Temporal Beam” Collimation/Spectral Focusing 160 6.4.2 Femtosecond Pulse Compression 161 6.4.3 Classic and “All-Fiber” Spectral Compression 163 6.4.4 Spectral Self-Compression: Spectral Analogue of Soliton-Effect Compression 165 6.4.5 Aberration-Free Spectral Compression with a Similariton-Induced Time Lens 167 6.4.6 Frequency Tuning Along with Spectral Compression in Similariton-Induced Time Lens 168 6.5 Similariton for Femtosecond Pulse Imaging and Characterization 172 6.5.1 Fourier Conversion and Spectrotemporal Imaging in SPM/XPM-Induced Time Lens 173 6.5.2 Aberration-Free Fourier Conversion and Spectrotemporal Imaging in Similariton-Induced Time Lens: Femtosecond Optical Oscilloscope 177 6.5.3 Similariton-Based Self-Referencing Spectral Interferometry 181 6.5.4 Simple Similaritonic Technique for Measurement of Femtosecond Pulse Duration, an Alternative to the Autocorrelator 185 6.5.5 Reverse Problem of NL-D Similariton Generation 187 6.5.6 Pulse Train Shaped by Similaritons’ Superposition 188 6.6 Conclusion 190 References 191 7 Applications of Nonlinear Optical Fibers and Solitons in Biophotonics and Microscopy 199 Esben R. Andresen and Hervé Rigneault 7.1 Introduction 199 7.2 Soliton Generation 200 7.2.1 Fundamental Solitons 200 7.2.2 A Sidenote on Dispersive Wave Generation 202 7.2.3 Spatial Properties of PCF Output 204 7.3 TPEF Microscopy 204 7.4 SHG Microscopy 205 7.5 Coherent Raman Scattering 206 7.6 MCARS Microscopy 207 7.7 ps-CARS Microscopy 210 7.8 SRS Microscopy 211 7.9 Pump-Probe Microscopy 213 7.10 Increasing the Soliton Energy 215 7.10.1 SC-PBG Fibers 216 7.10.2 Multiple Soliton Generation 217 7.11 Conclusion 218 References 218 8 Self-Organization of Polarization State in Optical Fibers 225 Julien Fatome and Massimiliano Guasoni 8.1 Introduction 225 8.2 Principle of Operation 227 8.3 Experimental Setup 229 8.4 Theoretical Description 230 8.5 Bistability Regime and Related Applications 234 8.6 Alignment Regime 238 8.7 Chaotic Regime and All-Optical Scrambling for WDM Applications 241 8.8 Future Perspectives: Towards an All-Optical Modal Control in Fibers 247 8.9 Conclusion 250 Acknowledgments 251 References 251 9 All-Optical Pulse Shaping in the Sub-Picosecond Regime Based on Fiber Grating Devices 257 María R. Fernández-Ruiz, Alejandro Carballar, Reza Ashrafi, Sophie LaRochelle, and JoséAzaña 9.1 Introduction 257 9.2 Non-Fiber-Grating-Based Optical Pulse Shaping Techniques 258 9.3 Motivation of Fiber-Grating Based Optical Pulse Shaping 260 9.3.1 Fiber Bragg Gratings (FBGs) 264 9.3.2 Long Period Gratings (LPGs) 267 9.4 Recent Work on Fiber Gratings-Based Optical Pulse Shapers: Reaching the Sub-Picosecond Regime 268 9.4.1 Recent Findings on FBGs 268 9.4.2 Recent Findings on LPGs 276 9.5 Advances towards Reconfigurable Schemes 284 9.6 Conclusion 285 References 285 10 Rogue Breather Structures in Nonlinear Systems with an Emphasis on Optical Fibers as Testbeds 293 Bertrand Kibler 10.1 Introduction 293 10.2 Optical Rogue Waves as Nonlinear Schrödinger Breathers 295 10.2.1 First-Order Breathers 295 10.2.2 Second-Order Breathers 301 10.3 Linear-Nonlinear Wave Shaping as Rogue Wave Generator 303 10.3.1 Experimental Configurations 304 10.3.2 Impact of Initial Conditions 306 10.3.3 Higher-Order Modulation Instability 308 10.3.4 Impact of Linear Fiber Losses 309 10.3.5 Noise and Turbulence 311 10.4 Experimental Demonstrations 311 10.4.1 Peregrine Breather 312 10.4.2 Periodic First-Order Breathers 313 10.4.3 Higher-Order Breathers 315 10.5 Conclusion 317 Acknowledgments 318 References 318 11 Wave-Breaking and Dispersive Shock Wave Phenomena in Optical Fibers 325 Stefano Trillo and Matteo Conforti 11.1 Introduction 325 11.2 Gradient Catastrophe and Classical Shock Waves 326 11.2.1 Regularization Mechanisms 327 11.3 Shock Formation in Optical Fibers 329 11.3.1 Mechanisms of Wave-Breaking in the Normal GVD Regime 330 11.3.2 Shock in Multiple Four-Wave Mixing 333 11.3.3 The Focusing Singularity 335 11.3.4 Control of DSW and Hopf Dynamics 336 11.4 Competing Wave-Breaking Mechanisms 337 11.5 Resonant Radiation Emitted by Dispersive Shocks 338 11.5.1 Phase Matching Condition 339 11.5.2 Step-Like Pulses 340 11.5.3 Bright Pulses 341 11.5.4 Periodic Input 342 11.6 Shock Waves in Passive Cavities 343 11.7 Conclusion 345 Acknowledgments 345 References 345 12 Optical Wave Turbulence in Fibers 351 Antonio Picozzi, Josselin Garnier, Gang Xu, and Guy Millot 12.1 Introduction 351 12.2 Wave Turbulence Kinetic Equation 354 12.2.1 Supercontinuum Generation 354 12.2.2 Breakdown of Thermalization 360 12.2.3 Turbulence in Optical Cavities 365 12.3 Weak Langmuir Turbulence Formalism 371 12.3.1 NLS Model 372 12.3.2 Short-Range Interaction: Spectral Incoherent Solitons 372 12.3.3 Long-Range Interaction: Incoherent Dispersive Shock Waves 375 12.4 Vlasov Formalism 378 12.4.1 Incoherent Modulational Instability 380 12.4.2 Incoherent Solitons in Normal Dispersion 381 12.5 Conclusion 384 Acknowledgments 385 References 385 13 Nonlocal Disordered Media and Experiments in Disordered Fibers 395 Silvia Gentilini and Claudio Conti 13.1 Introduction 395 13.2 Nonlinear Behavior of Light in Transversely Disordered Fiber 396 13.3 Experiments on the Localization Length in Disordered Fibers 399 13.4 Shock Waves in Disordered Systems 403 13.5 Experiments on Shock Waves in Disordered Media 407 13.5.1 Experimental Setup 407 13.5.2 Samples 407 13.5.3 Measurements 409 13.6 Conclusion 412 Acknowledgments 413 References 413 14 Wide Variability of Generation Regimes in Mode-Locked Fiber Lasers 415 Sergey V. Smirnov, Sergey M. Kobtsev, and Sergei K. Turitsyn 14.1 Introduction 415 14.2 Variability of Generation Regimes 417 14.3 Phenomenological Model of Double-Scale Pulses 425 14.4 Conclusion 428 Acknowledgments 429 References 429 15 Ultralong Raman Fiber Lasers and Their Applications 435 Juan Diego Ania-Castañón and Paul Harper 15.1 Introduction 435 15.2 Raman Amplification 436 15.3 Ultralong Raman Fiber Lasers Basics 439 15.3.1 Theory of Ultralong Raman Lasers 439 15.3.2 Amplification Using URFLs 444 15.4 Applications of Ultralong Raman Fiber Lasers 452 15.4.1 Applications in Telecommunications 453 15.4.2 Applications in Sensing 455 15.4.3 Supercontinuum Generation 455 15.5 Conclusion 456 References 456 16 Shaping Brillouin Light in Specialty Optical Fibers 461 Jean-Charles Beugnot and Thibaut Sylvestre 16.1 Introduction 461 16.2 Historical Background 462 16.3 Theory 463 16.3.1 Elastodynamics Equation 463 16.4 Tapered Optical Fibers 465 16.4.1 Principles 465 16.4.2 Experiments 466 16.4.3 Numerical Simulations 467 16.4.4 Photonic Crystal Fibers 469 16.5 Conclusion 473 References 474 Index 477

About the Author :
Edited by Sonia Boscolo, Aston Institute of Photonic Technologies, Aston University, Birmingham, UK Christophe Finot, Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS-Université de Bourgogne, Dijon, France